Magic Squares Wheel Method-Redux Part II

New Variants of Order 5

The wheel method is a means of constructing magic squares by a random access means instead of sequentially like the Loubère and Méziriac methods which has been rewritten in a more simplified form. The method patially fills up a square to form a wheel structure using numbers chosen from a complementary table of order n then randomly fills up the rest of the square with numbers chosen from whatever is left in the complementary table. This paper is a simplification of the original paper taking a more facile approach.

Three 5^th order variants have been constructed that differ from the original at the left diagonal. These three variants are the Reverse: 12 → 11 → 13 → 15 → 14, the Forward II: 11 → 14 → 13 → 12 → 15 and the Reverse II: 12 → 15 → 13 → 11 → 14, where these sequences are chosen from the values ½(n²-n+2) to ½(n²+n).

The squares are filled according to the method employed previously first forming the wheel structure and then filling in randomly the "non-spoke" values i.e., white cells chosen from pairs of numbers from the complementary table. Variants 2 and 4 place the complementary pairs across the square, for example {18,8}, and these end up as border squares. Placing the complementary pairs on the same row, again {18,8}, produces the Variant 3 non border square.

The complementary 5^th order employed for construction of these variants is shown below where the value in the top strand is complementary to the value in the bottom strand:

The next page uses variants 2, 3 and 4 of 7x7 squares.
Go to previous page . Go back to homepage.